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 NYSED is working on an initiative to translate the mathematics curriculum modules into the top 5 languages spoken in New York State, including Spanish, Chinese (Simplified and Traditional), Arabic,...

 Audience: Principals and Superintendents Description Understand the role that school and district leaders play in establishing and maintaining systems of datadriven instruction and inquiry....

 The Board of Regents (BOR) adopted the Common Core State Standards in July 2010 and in January 2011, the Board adopted the NYS P12 Common Core Learning Standards (CCLS), which include the Common...

 Performance Level Descriptions Performance Level Descriptions (PLDs) describe the range of knowledge and skills students should demonstrate at a given performance level. How were the PLDs developed...

 Student Outcomes Students use tangent segments and radii of circles to conjecture and prove geometric statements, especially those that rely on the congruency of tangent segments to a circle from a...

 Geometry Module 5: Circles With and Without Coordinates This module brings together the ideas of similarity and congruence and the properties of length, area, and geometric constructions studied...

 Geometry Module 4: Connecting Algebra and Geometry Through Coordinates In this module, students explore and experience the utility of analyzing algebra and geometry challenges through the framework...

 Geometry Module 3: Extending to Three Dimensions Module 3, Extending to Three Dimensions, builds on students’ understanding of congruence in Module 1 and similarity in Module 2 to prove volume...

 Geometry Module 2: Similarity, Proof, and Trigonometry Just as rigid motions are used to define congruence in Module 1, so dilations are added to define similarity in Module 2. To be able to discuss...

 Geometry Module 1: Congruence, Proof, and Constructions Module 1 embodies critical changes in Geometry as outlined by the Common Core. The heart of the module is the study of transformations and the...

 Student Outcomes Inscribe a rectangle in a circle. Understand the symmetries of inscribed rectangles across a diameter.

 In order to assist educators with the implementation of the Common Core, the New York State Education Department provides curricular modules in P12 English Language Arts and Mathematics that schools...

 Updated Modules and Curricular Resources The tables below reflect Mathematics and English Language Arts curricular materials and resources that have been updated. As additional materials are updated...

 Student Outcomes Students show that a quadrilateral is cyclic if and only if its opposite angles are supplementary. Students derive and apply the area of cyclic quadrilateral ABCD as 1/2 AB·CD·sin(w...

 Student Outcomes Students determine the area of a cyclic quadrilateral as a function of its side lengths and the acute angle formed by its diagonals. Students prove Ptolemy’s theorem, which states...

 Topic D brings in coordinate geometry to establish the equation of a circle. Students solve problems to find the equations of specific tangent lines or the coordinates of specific points of contact...

 Student Outcomes Students write the equation for a circle in centerradius form, (x  a)2 (y  b)2 = r2 using the Pythagorean theorem or the distance formula. Students write the equation of a circle...

 Student Outcomes Students complete the square in order to write the equation of a circle in centerradius form. Students recognize when a quadratic in x and y is the equation for a circle.

 Student Outcomes Given a circle, students find the equations of two lines tangent to the circle with specified slopes. Given a circle and a point outside the circle, students find the equation of the...

 The module concludes with Topic E focusing on the properties of quadrilaterals inscribed in circles and establishing Ptolemy's theorem. This result codifies the Pythagorean theorem, curious facts...

 Student Outcomes Students use the inscribed angle theorem to prove other theorems in its family (different angle and arc configurations and an arc intercepted by an angle at least one of whose rays...

 Student Outcomes Students understand that an angle whose vertex lies in the interior of a circle intersects the circle in two points and that the edges of the angles are contained within two secant...

 Student Outcomes Students find the measures of angle/arcs and chords in figures that include two secant lines meeting outside a circle, where the measures must be inferred from other data.

 Student Outcomes Students find “missing lengths” in circlesecant or circlesecanttangent diagrams.